Actually, this is not correct, at least going from the Navy to the Air Force. A Naval Aviator or Flight Officer officer flying on exchange status in the Air Force does not wear Air Force wings.
If the Naval Aviator or Flight Officer joins the Air Force, by resigning his commision in the Navy and accepting a commision in the Air Force, and serves in a flying position in the Air Force, then the Naval Aviator or Flight Officer is awarded the Air Force Pilot or Navigator rating by the Air Force.
Because the Air Force Pilot or Navigator designation is an Aeronautical Rating, awarded by the Air Force, and supported by important paperwork (medical certification, flight pay eligibility, etc.), a set of wings cannot simply be worn, nor is it temporary.
The Air Force allows Naval Aviators and Flight Officers to wear both set of wings on their uniform. A Naval Aviator or Flight Officer who is not filling a Pilot or Navigator position is allowed to continue to wear their Navy wings.
A Navy, Marine Corps, or Coast Guard exchange pilot serving with the Air Force continues to be a Navy, Marine Corps, or Coast Guard officer. They wear their service's uniform, their service's ribbons and medals, and their service's wings.
I served in an Air Force unit with a Naval Aviator exchange officer, in fact I was crewed with him during a two month rotation supporting Operation Southern Watch. I also know four Naval Aviators and one Naval Flight Officer who have made the transition to fly in the Air Force Reserve and Air National Guard, and I know an Air Force opthamologist who was a Naval Flight Officer prior to joining the Air Force medical corps.